Atrisiniet y^2x+y=x+y^2

$${ y }^{ 2 } x+y=x+ { y }^{ 2 }$$

Atrast x (complex solution)

$$\left\{\begin{matrix}x=\frac{y}{y+1}\text{, }&y\neq -1\\x\in \mathrm{C}\text{, }&y=1\end{matrix}\right,$$

Lineāra vienādojuma risināšanas darbības

Atņemiet x no abām pusēm.

$$y^{2}x+y-x=y^{2}$$

Atņemiet y no abām pusēm.

$$y^{2}x-x=y^{2}-y$$

Savelciet visus locekļus, kuros ir x.

$$\left(y^{2}-1\right)x=y^{2}-y$$

Daliet abas puses ar y^{2}-1.

$$\frac{\left(y^{2}-1\right)x}{y^{2}-1}=\frac{y\left(y-1\right)}{y^{2}-1}$$

Dalīšana ar y^{2}-1 atsauc reizināšanu ar y^{2}-1.

$$x=\frac{y\left(y-1\right)}{y^{2}-1}$$

Daliet y\left(-1+y\right) ar y^{2}-1.

$$x=\frac{y}{y+1}$$

Atrast x

$$\left\{\begin{matrix}x=\frac{y}{y+1}\text{, }&y\neq -1\\x\in \mathrm{R}\text{, }&y=1\end{matrix}\right,$$

Lineāra vienādojuma risināšanas darbības

Atņemiet x no abām pusēm.

$$y^{2}x+y-x=y^{2}$$

Atņemiet y no abām pusēm.

$$y^{2}x-x=y^{2}-y$$

Savelciet visus locekļus, kuros ir x.

$$\left(y^{2}-1\right)x=y^{2}-y$$

Daliet abas puses ar y^{2}-1.

$$\frac{\left(y^{2}-1\right)x}{y^{2}-1}=\frac{y\left(y-1\right)}{y^{2}-1}$$

Dalīšana ar y^{2}-1 atsauc reizināšanu ar y^{2}-1.

$$x=\frac{y\left(y-1\right)}{y^{2}-1}$$

Daliet y\left(-1+y\right) ar y^{2}-1.

$$x=\frac{y}{y+1}$$

Atrast y

$$\left\{\begin{matrix}\\y=1\text{, }&\text{unconditionally}\\y=-\frac{x}{x-1}\text{, }&x\neq 1\end{matrix}\right,$$